Group Classification of Differential-difference Equations： Low-dimensional Lie Algebras  

作　　者：Shou-feng SHEN Yong-yang JIN 

机构地区：[1]Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China

出　　处：《Acta Mathematicae Applicatae Sinica》2017年第2期345-362,共18页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(No.11001240,11371323)

摘　　要：Differential-difference equations of the form un = Fn（t, un-1,Un,Unn＋1,Un-1,un,Un＋1） are clas- sifted according to their intrinsic Lie point symmetries, equivalence group and some low-dimensional Lie algebras including the Abelian symmetry algebras, nilpotent nonAbelian symmetry algebras, solvable symmetry algebras with nonAbelian nilradicals, solvable symmetry algebras with Abelian nilradicals and nonsolvable symmetry al- gebras. Here Fn is a nonlinear function of its arguments and the dot over u denotes differentiation with respect to t.Differential-difference equations of the form un = Fn（t, un-1,Un,Unn＋1,Un-1,un,Un＋1） are clas- sifted according to their intrinsic Lie point symmetries, equivalence group and some low-dimensional Lie algebras including the Abelian symmetry algebras, nilpotent nonAbelian symmetry algebras, solvable symmetry algebras with nonAbelian nilradicals, solvable symmetry algebras with Abelian nilradicals and nonsolvable symmetry al- gebras. Here Fn is a nonlinear function of its arguments and the dot over u denotes differentiation with respect to t.

关 键 词：group classification differential-difference equation equivalence group finite-dimensional Lie algebra. 

分 类 号：O152.5[理学—数学]